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  Global Iwasawa-decomposition of SL(n,AQ)

Ahlén, O. (in preparation). Global Iwasawa-decomposition of SL(n,AQ).

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-8117-E Version Permalink: http://hdl.handle.net/21.11116/0000-0002-E7BE-4
Genre: Paper

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1609.06621.pdf (Preprint), 223KB
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 Creators:
Ahlén, Olof1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: Mathematics, Number Theory, math.NT,High Energy Physics - Theory, hep-th,Mathematics, Group Theory, math.GR
 Abstract: We discuss the Iwasawa-decomposition of a general matrix in SL($n$, $\mathbb{Q}_p$) and SL($n$, $\mathbb{R}$). For SL($n$, $\mathbb{Q}_p$) we define an algorithm for computing a complete Iwasawa-decomposition and give a formula parameterizing the full family of decompositions. Furthermore, we prove that the $p$-adic norms of the coordinates on the Cartan torus are unique across all decompositions and give a closed formula for them which is proven using induction. For the case SL($n$, $\mathbb{R}$), the decomposition is unique and we give formulae for the complete decomposition which are also proven inductively. Lastly we outline a method for deriving the norms of the coordinates on the Cartan torus in the framework of representation theory. This yields a simple formula valid globally which expresses these norms in terms of the vector norms of generalized Pl\"ucker coordinates.

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 Dates: 2016-09-21
 Publication Status: Not specified
 Pages: 20 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1609.06621
URI: http://arxiv.org/abs/1609.06621
 Degree: -

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